Why does a one-layer hidden network get more robust to poor initialization with growing number of hidden neurons?
You grasped a bit of the answer.


  In the latter two cases the optimisation gets stuck in suboptimal local minima. 


When you have only 2 dimensions, a local minima exists. When you have more dimensions, this minima gets harder and harder to reach, as its likelihood decreases. Intuitively, you have a lot more dimensions through which you can improve than if you only had 2 dimensions.

The problem still exists, even with 1000 neurons you could find a specific set of weights which was a local minimum. However, it just becomes so much less likely.